The (almost) integral Chow ring of ℳ̅₃

This paper is the fourth in a series of four papers aiming to describe the (almost integral) Chow ring of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mover accent="true"> <m:mi mathvariant="script">M</m:mi> <m:mo>̄</m:mo> </m:mover> <m:mn>3</m:mn> </m:msub> </m:math> M̄₃ , the moduli stack of stable curves of genus 3. In this paper, we finally compute the Chow ring of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mover accent="true"> <m:mi mathvariant="script">M</m:mi> <m:mo>̄</m:mo> </m:mover> <m:mn>3</m:mn> </m:msub> </m:math> M̄₃ with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="double-struck">Z</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mn>6</m:mn> </m:mrow> <m:mo stretchy="false">]</m:mo> </m:mrow> </m:mrow> </m:math> Z[1/6] -coefficients.